Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares [Bookshelf

Abstract

The book consists of three parts. Part 1 focuses on vectors and their manipulation. Vector algebra, linear functions, linearization, inner products, norms, linear independence, the concept of a basis, and orthogonality are covered. Part 2 is devoted to matrices. Basic matrix operations (including a clear discussion of all four ways to interpret matrix multiplication), linear systems of equations, the QR factorization, and various matrix inverses (left, right, and pseudoinverses) are discussed. Part 3 covers least squares and emphasizes different approaches to finding xt. A notable feature of this book is the excellent end-ofchapter problem sets that span a wide range of interesting applications. A detailed solutions manual is also available to instructors. The book is clear and direct, written by experienced authors. The need for textbooks that show mathematics in action is also clear. Linear algebra has become more important to modern students (arguably, more important than calculus), partly because of the rise of data science and deep learning. Through it all, this wonderful subject retains the beauty of good mathematics.